This paper presents a model of centralized vote-trading in a legislature. In this model, legislators trade only with party leaders, who set prices at which they will buy needed vote-changes and sell promises to pass or defeat particular bills. Each legislator trades away votes on bills of little concern to him and of high concern to leaders, and purchases promises from the leaders to pass (or defeat) particular bills of high concern to the legislator, relative to the price the leguslator must pay.This model is intended as a formal representation of an 'efficient' and possibly desirable legislature; modifications are needed to make it useful in describing actual legislatures. However, some evidence is cited to show that this model better accords with reality than previous votetrading models.

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While dimensional studies of congressional voting find a single, ideological dimension, regression estimates find several constituency and party dimensions in addition to ideology. I rescale several unidimensional studies to show their increased classification success over the null hypothesis that votes are not unidimensional. Several null hypotheses are explored. With these null hypotheses, 66%–75% of nonunidimensional roll call votes are nevertheless correctly classified by one dimension. After the rescaling, one dimension succeeds in correctly classifying 25%–50% of the votes, and second and third dimensions are important.